you can't do this directly in Ubuntu. You could install
something like TrueCrypt to do the job for you, but that's a heavyweight
solution.

It might be simplest to just put the files you want to protect in a
password protected archive but beware, not all archive formats support
passwords. Personally, when I need to do this, I use 7zip, but you need
to install that from the repositories. I don't actually know which, if
any, of the 'out-of-the-box' archiving formats Ubuntu provides that
support passwords.